# STATS Problem Set 2015

Question

Problem Set

(I) Excel coding question:

1) (5 points)The average cost of a hotel room in New York is said to be $168 per night. To determine if this is true, a random sample of 200 hotels is taken and resulted in a sample mean of $172.50 and an S of $15.40. Test the appropriate hypotheses at ? = 0.05.

a. Please write Excel coding to complete this Hypothesis test using T approach.

b. Please writeExcel coding to complete this Hypothesis test usingP approach. Write a complete coding, no calculation is needed.

2) (5 points) A marketing company claims that it receives 8% responses from its mailing. To test this claim, a random sample of 500 were surveyed with 25 responses. Test at the ? = 0.05 significance level by the following coding:

H0:? = 0.08

H1:? ? 0.08

Z* = -2.47

=if (normsinv(Z*)=:% Attendance, .png”>= Salariesand .png”>=Spending:

Table(3)

Regression Statistics

Multiple R

0.7930

R Square

0.6288

Adjusted R Square

0.6029

Standard Error

10.4570

Observations

47

ANOVA

df

SS

MS

F

Significance F

Regression

3

7965.08

2655.03

24.2802

2.3853E-09

Residual

43

4702.02

109.35

Total

46

12667.11

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-753.4225

101.1149

-7.4511

2.88E-09

-957.3401

-549.5050

% Attendance

8.5014

1.0771

7.8929

6.73E-10

6.3292

10.6735

Salary

6.85E-07

0.0006

0.0011

0.9991

-0.0013

0.0013

Spending

0.0060

0.0046

1.2879

0.2047

-0.0034

0.0153

1.1 Referring to Table (3),interprethow the Attendance can affect to the percentage of students passing the proficiency test.

1.2 Referring to Table (3), explain the implication ofMultiple R Square and Adjusted R Square.

1.3 What is the difference between them?

1.4 Referring to Table (3), what is the value of the test statistics when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test? Using this test statistics to complete your hypothesis test and describe the test steps and your conclusion.

1.5 Referring to Table (3), what is thep-values of the test statistics when testing whether instructional spending per pupil, has any effect on percentage of students passing the proficiency test?

1.6 Referring to Table (3) perform a null hypothesis to test whether daily average of the percentage of students attending class has any effect on percentage of students passing the proficiency test? WHAT IS YOUR CONCLUSION? Specify and explain your reasons.

1.7 After the two hypothesis tests for.png”> , re-estimate to improve the regression model.

Please conduct a F-test for this regression model for the significance of all coefficients.png”> of the independent variables using the F-test information from above table. What is your result? Is it consistent with the results from T-tests?

(8 points) As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, and S2 = 25. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose?

(8 points) Pizza shop delivers pizza to students DOM. The shop manage intended to speed up the delivery time of a trip by paying tips for each trip. The records shows that up to current, the average time for each trip is 25 minutes. For a sample of 25, we calculated that the sample mean is 23.5, the sample standard deviation is 7. At the critical level of 5 percent, please conduct a Hypothesis Test for the above issue: If the tips have successfully speeded up the delivery? Please specify the complete process for each of the 6 steps of a Hypothesis Test.

3. (10 points) For long time people believe that college participation rate for male and female suppose to be equal. Recently, there is a impression that the participation rate for girls is significantly higher than the rate of boys. A 200 sample is collected and the sample rate for boys is 0.48. At a confidence level of 95%, please use Hypothesis tests for boys and girls to find out if this participation rate has been significantly changed.

Extra Credit Question. (10 point)

Using the given data set, develop a simple OLS regression model and evaluate the model in terms of:

1. Fitness,

2. Significance,

3. If the model meet the 4 assumptions: linearity, independence, homogeneity, normality). Show your result with graph and convincing, specific explanations.

DATA:

Hours

Feet

24.00

545

13.50

400

26.25

562

25.00

540

9.00

220

20.00

344

22.00

569

11.25

340

50.00

900

12.00

285

38.75

865

40.00

831

19.50

344

18.00

360

28.00

750

27.00

650

21.00

415

15.00

275

25.00

557

45.00

1028

29.00

793

21.00

523

22.00

564

16.50

312

37.00

757

32.00

600

34.00

796

25.00

577

31.00

500

24.00

695

40.00

1054

27.00

486

18.00

442

62.50

1249

53.75

995

79.50

1397

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